Oh if you are at QUB then Stranmillis PS would be my number one option. It is outstanding, they have a list but you may get bumped up a bit if you are staff at Queens. The downside of that area is that it is very expensive. South Belfast would definitely be my preferred location (lived there as a student) but most houses are HMO and they don't want families as they can charge students per room.
Forge PS is good as is Rosetta PS (one street away from Forge) Both are quite ethnically mixed so I would not anticipate any problems. Both of these are located off the Ormeau Road which over the last few years has become very ethnically mixed. There are a lot of Africans living in this area and houses are a good bit cheaper than S Belfast.
Regarding prep schools (I forgot Victoria College Prep off Lisburn road, South Belfast) don't assume they are better. I have friends whose children go to Victoria prep and Penrhyn. Victoria College is a very mixed school as it is a boarding school and on the league tables the prep is very good however, the class sizes are big (24+) and for me if I was paying £5k+ I would want a smaller class. A friend of mine sent hers there (she worked in QUB) and then moved them to Stranmillis and says that Stranmillis is a better school all round. My friend with her dd's in Penrhyn says it is very good, class sizes smaller but the fees have gone up substantially in the last few years which she isn't happy about. It is also a very white school which may or may not suit you (I personally always look for an ethnically/racially mixed school where my dc won't be othered)
Regarding Ards...what can I say? It just feels very small town and hate to say it but rather chavvy. I have had abuse quite a few times in Ards shopping centre so that has probably coloured my opinion. i grew up near Ards and people still refer to people of colour as 'darkies' 
If you have the money to go privately then I would 100% stay in Belfast. It has really changed in the last 5 years, there is a much wider noticeable change ethnically which is great.
Regarding rentals, it is very competitive ( we are renters) and we found that offering 3-6 months upfront puts you at the top of the list. The fact that you are an academic should help too. I don't recommend any particular estate agent but IME get all of your ducks in a row before you come to view the houses. Have your previous landlord's references and proof of salary ready to submit with your application form. All houses get advertised through propertynews/pal anyway so checking individual agencies does not offer an advantage.
Other areas you may like to consider are Four Winds (BT8) which has a very good primary called Cairnshill PS. Also Finaghy (BT10) is cheaper and Finaghy pS is also good. Both are about 10 mins drive from QUB.
Fane Street PS is actually 'good' but has a bad name I suspect because in recent years there has been a massive influx of Somali children and (white) 'locals' then moved their children out. As a result class sizes are fairly small so there is definitely no shortage of places.
I don't know where you are in England but NI is significantly behind say London or Birmingham in terms of racial integration, but it is making really good progress.
If money is no issue for you then by all means send them privately, however I don't know of any schools in Belfast that aren't at least 'good' so I really would not expect much difference between prep and state, other than perhaps nicer grounds. If you are considering Methody prep then go for Downey (which is located in Pirrie Park, BT6) rather than Fullerton as the grounds are far superior. Fullerton is a breeze block building with barely a playground whereas Downey House is set in lovely grounds.
Any other questions just ask.